The value of Exponential Function e^x can be expressed using following Taylor Series.
e^x = 1 + x/1! + x^2/2! + x^3/3! + ……
How to efficiently calculate the sum of above series?
The series can be re-written as
e^x = 1 + (x/1) (1 + (x/2) (1 + (x/3) (……..) ) )
Let the sum needs to be calculated for n terms, we can calculate sum using following loop.
for (i = n – 1, sum = 1; i > 0; –i )
sum = 1 + x * sum / i;
Following is implementation of the above idea.
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Output:
e^x = 2.718282
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